Lining up vertices/edges horizontally along a slanted object without altering the shape of the object?
The best option here IMO is to use a knife tool. Press K and place the knife icon on the vertex to snap to it. Then press C to make a straight cut. Then select the angled edge and press X-->Dissolve Edges.


To align other edge loops to the newly created horizontal one add an edge loop with Ctrl+R, press E and then F.